Reliable predictions for species range changes require a mechanistic understanding of range dynamics in relation to environmental variation. One obstacle is that most current models are static and confound occurrence with the probability of detecting a species if it occurs at a site. Here we draw attention to recently developed occupancy models, which can be used to examine colonization and local extinction or changes in occupancy over time. These models further account for detection probabilities, which are likely to vary spatially and temporally in many datasets. Occupancy models require repeated presence/absence surveys, for example checklists used in bird atlas projects. As an example, we examine the recent range expansion of hadeda ibises (Bostrychia hagedash) in South African protected areas. Colonization exceeded local extinction in most biomes, and the probability of occurrence was related to local climate. Extensions of the basic occupancy models can estimate abundance or species richness. Occupancy models are an appealing additional tool for studying species' responses to global change.